Methodology for Testing Hypotheses

12 • Paper Towel: In the paper towel category, we can use brand name, pricepromotion, and some brand-specific attributes e.g., plain white versus design, paper size as explanatory variables. Some sensory search attributes e.g., the exact design on the towel, its softness are missing online. Therefore, we expect paper towels with designs a sensory attribute to have lower impact on choice online, where the actual designs cannot be easily seen H1a, and for brand names to have higher impact online H2. Finally, we expect lower price sensitivity online H3.

3. Methodology for Testing Hypotheses

Description of data: To fully understand the differences in choice behavior induced by the shopping medium, we would ideally need to conduct a randomized experiment in which some people are assigned to shop online and some are assigned to shop offline over an extended period of time. Such an experiment would be expensive and impractical. A realistic and practical alternative is to use longitudinal field data from separate samples of online and offline shoppers, but account for self-selection differences between these samples in the methodologies we use for data analyses. This approach is quite common in many scientific fields where random assignments are not possible e.g., labor economics; see Heckman 1976, 1979. Not surprisingly, the composition of people who shop online is different from the composition of people who shop offline. To account for these sample differences, we do the following: 1 On aggregate, we try to match the samples on the education levels of the shoppers, an observable criterion, that differentiates between early adopters of the online shopping medium and the shoppers in traditional stores. Several surveys suggest that the online population is highly educated. For example, over 50 of those surveyed by the “GVU surveys” www.gvu.gatech.eduuser_surveys have college education or higher. 2 We incorporate within the model a term to account for the fact that household income may affect price sensitivity; 3 Even for these matched samples, and after accounting for observable differences, there may remain important unobservable differences e.g., in value of time that influence store choice. To address 13 this issue, we develop a new methodology to correct for selectivity bias in a choice model with unobserved heterogeneity. We formulate a two-stage choice model in which customers first choose the store type in which they shop online versus offline, and then make brand choices within their chosen store environment. In our estimation, we allow the first-stage errors to correlate with the unobserved heterogeneity distribution of parameters in the second stage. In what follows, we describe our methods in greater detail. For our study, we use two of the most comprehensive data sets currently available. The first data is from Peapod, where we tracked about 300 subscribers in the Chicago suburban area from May 1996 to July 1997 6 . The second data set is from IRI for 1,039 panelists who shopped in the same grocery chain in the same geographic area, although not in the same supermarket as the Peapod subscribers. The supermarket from which Peapod customers are served is not part of the sample of supermarkets that IRI uses to collect its panel data. These data were collected between September 1995 and November 1997 from three stores. Two of these supermarkets are located in the same part of the metropolitan area as the Peapod store and all are in relatively affluent areas. For the IRI data, we have individual-level demographic information for all the panelists. For the Peapod data, we have aggregate demographics based on a survey conducted by the company, and we have individual-level demographic data for only about 40 of the panelists. For the remaining individuals, income data was imputed as the overall average for Peapod consumers in the Chicago area. Table 1 summarizes some demographic information for the two samples that we used in our analyses. An examination of Table 1 suggests that Peapod households are, on the average, -------------------- Table 1 here -------------------- 6 These panelists are a subset of active Peapod households that do a majority of their grocery shopping through Peapod. The average order size for these panelists is around 125, about five times 23.5, the size of the average order in a regular grocery store. The average Peapod “visit” lasts 23 minutes in our sample with improved modem speeds, this has probably declined. In comparison, a visit to a regular store lasts about 1 hour Bauer, 1995. An average order in Peapod contains 42 items, and the average number of visits per month is 2.2. Consumers visit regular grocery stores about 7.9 times per month on the average Food Beverage Marketing, August 1998. 14 younger, better educated, and more affluent than the US population. Also, a larger proportion of Peapod households have children. To get some comparability between the samples used in the analyses, we use education as a matching criterion and retain only those IRI households with at least one member having graduated from college denoted as IRI H-E. It was important to match on the education criterion because only about 20 of the IRI sample had some college education compared to about 95 in the Peapod panel. With regard to income, the Peapod sample is much more affluent, even when compared to the IRI H-E sample. 7 These income differences could induce differences in choice behavior, because higher income households face substantially different budget constraints. To account for the effects of budgetary considerations on price sensitivity, we include a price-income interaction term in our models see Kalyanam and Putler 1997. This is described in the subsections below. Two-Stage Choice Model: Consumer price sensitivity is likely to be a function of income, an observable characteristic of the household. However, other variables that remain unobserved by the researcher are also likely to affect price sensitivity. When these unobserved variables do not affect the choice of store type online vs. offline, they would have the same distribution in the Peapod and IRI H-E samples and, thus, cannot be a source of differences in behavior between samples. However, it is likely that some of the unobserved variables may also affect store choice. For example, some households where both adults are employed may have a higher “opportunity cost of time,” due to availability of overtime work opportunities. To save time, these households are more likely to shop online, and are also more likely to be less price sensitive than other households with the same observable demographics e.g., income. As a result, this self-selection along unobserved characteristics during store choice may be responsible for differences in price sensitivities between online and offline samples. This self-selection bias must be removed before we can attribute differences in parameter estimates to differences in the store environment. 7 Although there are some differences in category definitions and the times at which the income data were collected for the three groups in Table 1, it is nevertheless clear that Peapod members are significantly more affluent. Unfortunately, we do not have any psychographics information e.g., price sensitivity, or information on computer skills or interest e.g., subscription to a computer magazine for the respondents in either sample. 15 The outcome of store choice i.e., shop online or offline provides information about those unobservable characteristics that may affect price sensitivities in brand choices. This potential relationship is captured in a two-stage choice model. In the first stage, we use a binary probit model of store choice online versus offline, with utility for shopping online vs. offline being a function of household income. In the second stage, we use a multinomial logit model of brand choice with observed and unobserved heterogeneity. For reasons mentioned above, the errors from the binary probit model are likely to be correlated with the unobserved heterogeneity in price sensitivity i.e., heterogeneity not induced by differences in observed characteristics, such as income during brand choice. We remove self-selection bias by taking this correlation into account in the estimation procedure described below. Our methodology contains two novel aspects, which distinguish it from previously proposed methods dealing with self-selection Heckman 1976, 1979; Lee 1983; Trost and Lee 1984. The previous methods incorporate a simple regression model i.e., with fixed coefficients in the second stage. This approach, with a second-stage regression model, has also been used in Marketing e.g., Krishnamurthi and Raj 1988. In contrast, in the second stage, our method accommodates a multinomial choice model with unobserved heterogeneity. Also, while the previous methods simply allow correlations between errors of the two stages, our method performs bias correction on specific parameters e.g., price sensitivity. As described below, we have to use more sophisticated estimation methods to estimate our two-stage model. First Stage Choice Model: The store choice model is a binary probit with the following structure: U online,i = γ + γ 1 ⋅ HHI i + ξ i 2 U online,i is the utility that consumer i gets from shopping online, rather than offline; HHI i is household income of consumer i , ξ i is standard Normal error. Consumer i chooses to shop online if and only if U online,i 0. This model is estimated on the joint data from the IRI and Peapod samples, separately from, and prior to estimating the second stage, and yields the point estimates 16 γ ˆ and γ ˆ 1 . Conditional on store choice, error ξ i comes from a truncated standard Normal distribution, such that ξ i - γ ˆ - γ ˆ 1 ⋅ HHI i if consumer i shops online and ξ i - γ ˆ - γ ˆ 1 ⋅ HHI i if consumer i shops offline. This constraint will be applied in the second stage choice model. Second Stage Choice Model: To formulate the brand choice model, we follow Russell and Kamakura 1993 and first decompose brand value BV into two components: a tangible component BTV and an intangible component BIV. The tangible value can be directly attributed to levels of measurable attributes e.g., fat per serving, while the intangible value cannot be captured by the measured attributes. The impact of brand name on choice is captured by the intangible value. Let J and K be the number alternatives and brands, respectively, in the choice set. First, consider product categories where each alternative in a choice set is associated with a distinctly different brand i.e., there is no distinction between a brand and a choice alternative and J=K. This is the case in our analysis of the margarine category. Then, brand j’s utility during choice occasion n is specified by a linear utility function for ease of exposition, we suppress household subscript i: U jn = BIV j + BTV j + ß·X jn + e jn j =1,…,J 3 where X jn is a vector of marketing variables e.g., price, promotion or household income e.g., price × income, ß is a row vector of consumer sensitivities, and e jn is the random component of U jn . By relating the tangible component to measurable attributes, equation 4 becomes: U jn = BIV j + g.A j + ß·X jn + e jn 4 where A j is a vector of attributes e.g., fat content, presence of bleach, g is a row vector of consumer sensitivities to those attributes. Let R be the number of brand-specific attributes 17 included in the analysis i.e., the sizes of A j and g . Because of standard identification constraints, only J-1-R brand-specific coefficients i.e, BIV j ′ s and elements in g can be identified. Following Kamakura and Russell 1993, we impose: å j BIV j = 0 5 and å j BIV j ·A jr = 0; r=1,…,R 6 The identification constraints in 5 and 6 ensure that brand intangible values are orthogonal to brand-specific attributes. Kamakura and Russell 1993 estimate the parameters sequentially, with sensitivities to marketing mix variables estimated first, and brand intangible values and sensitivities to product attributes estimated second. We, however, estimate all the coefficients simultaneously. This approach allows us to derive the statistical properties based on asymptotic standard errors andor likelihood ratio tests of the brand intangible values and sensitivities to product attributes. Second , consider product categories where there are several choice alternatives for each brand i.e., JK. Alternatives belonging to the same brand k now share that brand’s intangible brand value BIV k which replaces BIV j in equations 3 - 4. If J-K ≥ R, as is the case in the detergent and paper towel categories, all coefficients in the model are identified except for one brand intangible value. To identify the model, we set the brand intangible value of the brand with the largest market share to zero. Note that in the utility specification given in 4, we cannot identify the importance weights of the information integration model, α i , as specified in 1. The α parameters are subsumed within the coefficients given in 4. 8 There are also other factors that prevent us from directly estimating and comparing the importance weights across the online and offline models: i the information integration model specified in 1 does not have an error term, which we need for 8 Specifically, for linear utility models, the ith component of 1 is , X s X s X U i i i i i i i i i α = α = α where s i is a scaling factor for the utility measure. The corresponding term in the measurement model 4 is given by , X i i β so that β i captures the effect of both α i and s i . 18 estimating choice models. ii The basic information integration model also does not incorporate heterogeneity in preference structures, which we incorporate in our choice models. For these reasons, we will compare the relative importance of attributes online and offline using other measures, such as the estimated proportion of households exhibiting positive vs. negative coefficients for a specific attribute, or their responses to identical promotions. We must point out that the purpose of our analysis is not to test the information integration theory, but only to test the implications of this theory as summarized in our hypotheses. For this objective, our approach is appropriate. Modeling Heterogeneity: We consider two types of heterogeneity: brand intercept heterogeneity referred to as preference heterogeneity by Papatla 1996 and response heterogeneity. The former characterizes the distribution of brand intercepts i.e., brand intrinsic values across consumers whereas the latter characterizes the distributions across consumers of such factors as price sensitivity and response to brand-specific attributes. We include intercept heterogeneity in all our models. We selectively include response heterogeneity in our models when both the online and offline samples are large enough to yield reliable estimates. 9 We assume a multivariate Normal distribution of parameters and IID extreme value errors. This yields a heterogeneous logit model, which we estimate using simulated maximum likelihood method Erdem 1996. However, in our case we also need to account for, and estimate the correlation of first choice errors with unobserved heterogeneity in price sensitivity in the second stage. We accomplish this by making random draws from the distribution of heterogeneity, which in fact, is the basis for simulated maximum likelihood estimation. Specifically, we obtain draws from the simulated heterogeneity distribution for price sensitivity through rejection sampling, such that the realizations of our random draws are consistent with the corresponding store choice error. A pair {price sensitivity coefficient, store choice error} is drawn from their unconditional bivariate Normal distribution. If the draw yields a valid store choice error i.e., ξ i - γ ˆ - γ ˆ 1 ⋅ HHI i for 9 Heterogeneity-related parameters capture differences across individuals, rather than across choice occasions. Thus, we need larger samples of panelists to assess heterogeneity along more dimensions. In our models, we ensured that there were at least ten panelists for each heterogeneity-related parameter. 19 consumers shopping online and ξ i - γ ˆ - γ ˆ 1 ⋅ HHI i for consumers shopping offline, the corresponding price sensitivity is retained. Otherwise that particular realization is discarded. We continue the process until we obtain the desired number of price sensitivities here, 50. This procedure yields estimates that are corrected for self-selection bias for the population parameters i.e., the means and covariance matrix of the Multivariate Normal distribution 10 .

4. Results